To solve the system of equations using substitution, we isolate one variable in one equation and substitute it into the other equation. After performing the necessary steps, we find that the solution to the given system of equations is x = 1 and y = 2.
To solve the system of equations using substitution, we need to isolate one variable in one equation and substitute it into the other equation. Let's solve the given system of equations step by step:
1. Start with the first equation: x - 4y = -7.
2. Solve for x in terms of y by adding 4y to both sides of the equation:
x = 4y - 7.
3. Now, substitute this expression for x in the second equation: 6x + 6y = 18.
Replace x with 4y - 7:
6(4y - 7) + 6y = 18.
4. Simplify the equation by distributing and combining like terms:
24y - 42 + 6y = 18.
30y - 42 = 18.
5. Add 42 to both sides of the equation:
30y = 60.
6. Divide both sides of the equation by 30 to solve for y:
y = 2.
7. Substitute the value of y back into the first equation to solve for x:
x - 4(2) = -7.
x - 8 = -7.
x = 1.
8. So, the solution to the system of equations is x = 1 and y = 2.